From The British Library's collection of public domain images on Flickr, Edwin Burrage, 'Gerard Mastyn, the Son of a Genius', p. 75.

Teaching vibrato is one area where I feel I can never have enough resources. In this article, I share the two exercises I use to introduce students to the movements involved in creating vibrato. However you choose to apply vibrato, and the historical issues involved, are another discussion - but I do think that students should be able to play with a constant vibrato as a first step, developing a more varied approach to its application later.

Polishing / dusting the fingerboard

This exercise develops the up and down movement made by the hand in vibrato, and it is often the first introduction I offer to vibrato.

Move the left hand up and down the fingerboard rapidly, as if polishing or dusting the fingerboard with the palm of the hand. Use the full range of positions from 1-4 - let the hand rebound back up from the side of the cello as it reaches the fourth position

Gradually decrease the range of the polishing movement to roughly one position

Stop to play a note, any note, in any position you choose, but keep the ‘polishing’ movement going with the hand: the knuckles and hand should be moving up and down while you stop the note with your finger, and the elbow and forearm should stay relaxed, and freely following the movement in the fingers/ hand

Try this exercise with all fingers

NB: Initially students may need help with bowing while doing vibrato, as the movements involved on each side (left/right) are quite different.

Oscillations in time

Pick a note

Do vibrato at such a slow pace that you have four evenly spaced oscillations. Imagine each vibrato movement of the knuckle downwards and back up again is a crotchet, in a bar of 4/4 time. Each movement should be loose: imagine a very slow waving movement of the hand (waving with palm faced inwards towards the fingerboard)

Now speed this movement up to quavers, keeping the same pulse

And to triplets

And semiquavers

As with the last exercise, aim to keep the forearm and the elbow relaxed

Are you a cellist, and do you have to find some music to play at a wedding? That was me a few months ago.
My brief was Bach; instrumentation cello and piano.
These two books are the ones I went with - the writing is excellent, and the level for these pieces is probably around Grade 4-6 AMEB, so quite playable and complex enough to sound good in performance!